Stable comodule deformations and the synthetic Adams-Novikov spectral sequence

2024/02/22 by J. Francis Baer, Baer, J. Francis, Maxwell E. Johnson +3
Business, Management and Accounting · Engineering · Physics and Astronomy · #55P42 #55Q10 #55Q45 #55T15 #Algebraic Topology (math.AT) #Elasticity and Wave Propagation #FOS: Mathematics #Nonlinear Waves and Solitons #Optics and Image Analysis

paper · pdf · doi:10.48550/arxiv.2402.14274

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Adams-Novikov spectral sequence in \mathbbF_p-synthetic spectra, computing the synthetic analogs of BP and its cooperations to identify the synthetic Adams-Novikov E₂-page, computed in a range with a synthetic algebraic Novikov spectral sequence. We then identify deformations associated to the Cartan-Eilenberg and algebraic Novikov spectral sequences in terms of stable comodule categories, categorifying an algebraic Novikov spectral sequence result of Gheorghe-Wang-Xu. We then apply Isaksen-Wang-Xu methods in \mathbbF₂-synthetic spectra to deduce differentials in the p=2 synthetic Adams-Novikov for the sphere, producing almost entirely algebraic computations through the 45-stem.

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